Structure of the theories of probability

Abstract

We examine the concept of probability from its emergence within the realm of the games of chance and the development of the theory of probability until the appearance of the treatise of Kolmogorov on this subject. The discipline related to that theory is framed as the science of aleatory events. Probability is understood as a primitive concept represented by a measure assigned to the space of events and obeying the fundamental postulates of the theory. The measurement of probability is the ratio of the number of the observed favorable outcomes and the total number of observed outcomes when these numbers are larger enough.

Study of static and dynamic properties of even-even 14–24O and 38–54Ca in the frame of Random Phase Approximation (RPA) method with different Skyrme parameterizations

“…excitation energies of the RPA modes are the corresponding eigenvalues [23], whose elements themselves are matrices, more derivative detailed about theory in [22,24]…”

“…The strength distribution energy-weighted sum rule (EWSR) is defined in terms of the first moment as (m 1 ). [31,32]; when general IS and IV external fields related sum rule properties [23] . It can be calculated using;…”

“…Higher modes of the excited states, energy-weighted sum rule, the centroid, constrained, and scaling energies of the resonances have been studied and illustrated together with available experimental data for comparison. For the low-lying excited states, the energy transition densities for J π = 2 + and J π = 3 − are reproduced well in [18][19][20][21][22][23][24] O and 46-54 Ca isotopes. The neutron single particle states as a function of neutron number have been also presented.…”

“…The latter used the HF method with effective nucleon-nucleon interactions of the Skyrme types plus the RPA. The results of the calculations were obtained for various even-even nuclei such as [16][17][18][19][20][21][22][23][24][25][26][27][28] Pb, calculated within the fully self-consistent HF based RPA theory, using 33 different Skyrme parameterizations.…”

Theories of motion and matter from Aristotle to Galileo

“…Scientific theories underwent a great development in the seventeenth century [1][2][3][4][5][6][7][8][9][10][11][12]. A major development took place particularly in the theory of motion of bodies when Galileo proposed his kinetic theory of projectile motion and Newton introduced the dynamic theory of motion.…”